The most common malpractice is simply juggling "explanatory variables" until you get the result you wanted to get (or that you're "supposed" to get). The problem is that for many problems, there is only one limited data set, if that much, so little scope for testing a hypothesis more than once.
Another common transgression is using correlation to justify a particular direction of causation, notwithstanding the availability of (admittedly imperfect) tests for causation.
My favorite exercise was a paper by Edward Gramlich which did a regression with seven observations. At the other extreme, someone published a paper entitled "I Ran One Million Regressions," or something like that.
mbs